U.S. Sen. Lamar Alexander is beginning his re-election campaign with a three-to-one lead over his Republican primary opponents and other possible tea party contenders, according to a new poll paid for by the incumbent.

The poll, released Wednesday and conducted by North Star Opinion Research, a Republican polling firm, was taken Aug. 19-22, a stretch that overlaps with Carr’s announcement last week that he would ditch his U.S. House run for a shot at Alexander.

Carr, hoping to appeal to a frustrated base of tea party voters, kicked off his campaign by accusing the two-term senator of producing a record that is the “most liberal” of any Republican in Washington from Tennessee.

But other tea party candidates may still enter the contest. One of those considering a bid, Knox County Mayor Tim Burchett, is actually polling ahead of Carr.

In a one-on-one contest, Burchett would net 23 percent of the vote, the poll found, compared to 62 percent for the 73-year-old Alexander.

Long-shot candidate Brenda Lenard, who ran unsuccessfully against U.S. Sen. Bob Corker in last year’s GOP primary and has said she will run this year as well, trails Alexander, 69 percent to 16 percent.

Former Williamson County Republican Party chairman Kevin Kookogey had the worst showing of potential candidates included in the poll, with 15 percent to Alexander’s 69 percent.

Whit Ayres, president of North Star Opinion Research, said the poll shows that Alexander remains a “remarkably popular public official” while his challengers are “little known or completely unknown.”

Neither Burchett nor Kookogey ruled out runs when contacted lastt week by The Tennessean. On Saturday, more than 60 Tennessee tea party groups plan to meet in Nashville to begin a series of vetting sessions to coalesce around a consensus pick to challenge Alexander.

Carr seemed unfazed by the numbers outlined in the poll and said its release reflects the Alexander campaign’s “nervousness” over his entry into the race. “We’ve got some internal data, but we’re not releasing that to the public,” he said.

His campaign has cited data that suggest Alexander has favorability exceeding 60 percent, but those figures go down when Republican voters are reminded about certain votes.

To run a viable a campaign, any challenger would likely need to compete financially against Alexander, who has $3 million. That might require the help of groups from outside Tennessee.